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arxiv: 2605.08407 · v1 · submitted 2026-05-08 · 🌌 astro-ph.GA

Recognition: 2 theorem links

· Lean Theorem

The Peculiar Velocity of Messier~87 from Microarcsecond Geodetic VLBI Astrometry

Valeri V. Makarov , Phil Cigan , Kyle Corcoran
Authors on Pith no claims yet

Pith reviewed 2026-05-12 01:01 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords Messier 87peculiar velocityVLBI astrometryproper motionVirgo clustercosmic microwave backgroundtangential velocitygeodetic VLBI
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The pith

28 years of geodetic VLBI data yield a 1037 km/s peculiar velocity for M87 at 65° to the line of sight.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the proper motion of the radio core in Messier 87 using repeated high-precision positions from the global geodetic VLBI network spanning 28 years. A statistical fit with 1-norm optimization and bootstrapping gives a motion of 10.19 microarcseconds per year at position angle 189.2 degrees. Converting this angular speed with the adopted 16.1 Mpc distance produces a tangential velocity component of 787 km/s. Adding the known radial velocity relative to the cosmic microwave background rest frame produces a total peculiar velocity of roughly 1037 km/s directed 65 degrees from the current line of sight. This vector points roughly in the same direction as the expected bulk flow of the Virgo filament toward the Great Attractor, but is faster than the Milky Way's motion in that direction by about 470 km/s.

Core claim

The radio-emitting core of M87 exhibits a proper motion of 10.19 ± 0.64 μas yr⁻¹ at equatorial position angle 189.2° ± 3.5° in the ICRF. At a distance of 16.1 Mpc this corresponds to a tangential velocity of 787 ± 50 km s⁻¹. Combined with the known radial velocity, the total peculiar velocity vector relative to the CMB rest frame has a magnitude of approximately 1037 km s⁻¹ and lies at an angle of 65° to the present line of sight, implying a substantial tangential relative motion between M87 and the Milky Way.

What carries the argument

Robust 1-norm optimization plus bootstrapping applied to 28 years of repeated VLBI position measurements of the radio core to extract the proper-motion vector.

If this is right

  • M87 and the Milky Way possess a large relative tangential velocity component.
  • The direction of M87's peculiar velocity aligns with the reconstructed motion of the Virgo filament toward the Great Attractor.
  • The Milky Way's velocity in the same large-scale direction is slower than M87's by roughly 470 km/s.
  • Full three-dimensional velocities of dominant cluster galaxies can now be obtained from long-term geodetic VLBI campaigns.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the core truly represents the galaxy, similar VLBI campaigns on other nearby radio-loud ellipticals could map the local velocity field at higher precision than redshift surveys alone.
  • The measured offset from the Milky Way's motion may constrain the dynamical mass of the Virgo cluster or the gravitational influence of the Great Attractor.
  • Repeating the measurement with future higher-sensitivity arrays would test whether the current uncertainty of 50 km/s can be reduced enough to distinguish between different Lambda-CDM flow models.

Load-bearing premise

The measured motion of the compact radio core is assumed to trace the bulk peculiar motion of the entire galaxy rather than an internal jet feature.

What would settle it

A future optical or infrared astrometric campaign that measures the proper motion of M87's stellar population directly and finds a tangential velocity differing by more than 200 km/s from 787 km/s.

Figures

Figures reproduced from arXiv: 2605.08407 by Kyle Corcoran, Phil Cigan, Valeri V. Makarov.

Figure 1
Figure 1. Figure 1: Dots represent individual VLBI coordinate measurements obtained for M87 in right ascension (upper panel) and dec￾lination (lower panel) as functions of time. The sidewise histograms on the right are the sample distributions of these coordinate measurements. The colored circles are window-averaged values of the same measurements and highlight the underlying trends. Note that the scatter of individual data p… view at source ↗
Figure 2
Figure 2. Figure 2: VLBI time series positions on the sky for M87, smoothed with a 120-day window (P. Cigan et al. 2024). Time is denoted by the color scale, while gray background points represent the unsmoothed time series. This reveals clear coherent position variability on the order of ∼0.4 mas on several-year timescales. This figure is available as an 8-second animation in the online version of this article. In the animat… view at source ↗
Figure 3
Figure 3. Figure 3: Astrometric differential autoregressive functions of M87 in RA (x) and Dec (y) equatorial coordinates computed from 2269 24-hr VLBI sessions spanning 39 years. The specific algorithm used for this computation is described in Sect. 3. The nearly linear trend in dy indicates a measurable proper motion in Dec. The results of ADAF calculation are shown in Figs. 3 for each coordinate component. While the RA com… view at source ↗
Figure 4
Figure 4. Figure 4: Sample distribution of error-normalized astrometric offsets from the multi-decade mean position of the radio source M87. The magenta curve shows the expected Rayleigh[1] distribution if these bivariate values were Gaussian-distributed. The optimization problem splits into two separate fits. For a given set of coordinate measurements {xj , yj}, the nonlinear objective function is Ψ(x0, µx) = Xn j=1 |xj − xp… view at source ↗
Figure 5
Figure 5. Figure 5: Bootstrapped distributions of proper motion components of M87 estimated via Nelder-Meade 1-norm optimization. Each computation (out of 1001) uses a randomly selected subsample of 1134 non-repeating data points. 5 We used the Nelder-Mead method, which is the default in Wolfram Mathematica [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Composite image of M87 with the proper motion vector derived in this study. The component g, z, y filter images were extracted from the Pan-STARRS imaging facility available at https://ps1images.stsci.edu/cgi-bin/ps1cutouts. North is up, east is to the left, and the angular scale bar also describes the corresponding physical scales for the range of estimated distances to M87. The jet is seen at position an… view at source ↗
read the original abstract

Our knowledge of the space velocity of Messier 87, which is the dominant galaxy in the Virgo cluster, has been limited to the radial velocity component. Using a cadence of precision position measurements with the global geodetic very long baseline interferometry (VLBI) system over 28 years, we determined the proper motion vector of the radio-emitting core by a robust statistical method involving 1-norm optimization and bootstrapping. The proper motion vector is directed at a position angle $189.2\degr \pm 3.5\degr$ in the equatorial International Celestial Reference Frame, and its magnitude is $10.19$ $\mu$as yr$^{-1}$ with an uncertainty of $0.64$ $\mu$as yr$^{-1}$. The projected velocity of the AGN in the tangential sky plane is ($787\pm50$)~km~s$^{-1}$. The peculiar velocity of Messier 87 with respect to the preferred rest frame of the cosmic microwave background field is approximately 1037 km s$^{-1}$ (assuming a distance of 16.1 Mpc) with an angle of 65$^\circ$ to the current line of sight, which implies a tangential relative motion of M87 and the Galaxy. The peculiar velocity of M87 is directionally concordant with the reconstructed and $\Lambda$CDM-simulated motion of the Virgo filament towards the Great Attractor, but the Milky Way moves slower by 470 ~km~s$^{-1}$ in that direction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports a 28-year geodetic VLBI astrometric time series for the radio core of M87. Using 1-norm minimization and bootstrapping, the authors derive a proper motion of 10.19 ± 0.64 μas yr^{-1} at position angle 189.2° ± 3.5° in the ICRF. Converting the transverse component at an adopted distance of 16.1 Mpc yields 787 ± 50 km s^{-1}; combining with the known radial velocity produces a peculiar velocity vector of ~1037 km s^{-1} at 65° to the line of sight relative to the CMB frame. The result is interpreted as evidence for tangential motion between M87 and the Milky Way and directional agreement with the Virgo filament's motion toward the Great Attractor.

Significance. If the radio core motion accurately traces M87's center-of-mass velocity, the measurement supplies the first direct transverse-velocity constraint for the dominant Virgo galaxy. This would be valuable for calibrating local peculiar-velocity fields, testing ΛCDM predictions for the Virgo filament, and refining the relative motion between the Local Group and the Great Attractor. The robust 1-norm plus bootstrap fitting procedure is a clear methodological strength that reduces sensitivity to outliers in the long astrometric series.

major comments (2)
  1. [Results section (velocity conversion)] Results section (velocity conversion paragraph): the reported peculiar velocity of 1037 km s^{-1} and angle of 65° are computed at a fixed distance of 16.1 Mpc, yet the uncertainty on this distance is not propagated. Because both the tangential speed (v_t = 4.74 μ d) and the radial peculiar component (v_pec,r = v_rad − H_0 d) scale with d, the vector magnitude, direction, and the claimed 470 km s^{-1} differential with the Milky Way inherit this unquantified error; the abstract and main claims should reflect the propagated uncertainty.
  2. [Discussion section] Discussion section: the central claim that the measured core proper motion equals the bulk peculiar motion of M87 rests on the assumption that jet-induced core shifts and evolving components contribute negligibly. While the 1-norm + bootstrap method is robust, the manuscript does not quantify possible systematic offsets between the optically thick jet base and the stellar center of mass; this assumption is load-bearing for the interpretation of tangential motion and concordance with large-scale flows.
minor comments (1)
  1. [Abstract] Abstract: the proper-motion magnitude is written as '10.19 μas yr^{-1} with an uncertainty of 0.64 μas yr^{-1}' rather than the conventional '10.19 ± 0.64 μas yr^{-1}'; adopting standard notation would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. We address the two major comments point by point below. Where the comments identify clear omissions, we have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: Results section (velocity conversion paragraph): the reported peculiar velocity of 1037 km s^{-1} and angle of 65° are computed at a fixed distance of 16.1 Mpc, yet the uncertainty on this distance is not propagated. Because both the tangential speed (v_t = 4.74 μ d) and the radial peculiar component (v_pec,r = v_rad − H_0 d) scale with d, the vector magnitude, direction, and the claimed 470 km s^{-1} differential with the Milky Way inherit this unquantified error; the abstract and main claims should reflect the propagated uncertainty.

    Authors: We agree that the distance uncertainty must be propagated. The adopted distance of 16.1 Mpc carries a typical uncertainty of order 0.5 Mpc (~3%). In the revised manuscript we recompute the tangential velocity, peculiar-velocity vector magnitude, direction, and the differential with the Milky Way, folding in this error via standard propagation. The updated values and enlarged uncertainties will appear in the abstract, results, and discussion. revision: yes

  2. Referee: Discussion section: the central claim that the measured core proper motion equals the bulk peculiar motion of M87 rests on the assumption that jet-induced core shifts and evolving components contribute negligibly. While the 1-norm + bootstrap method is robust, the manuscript does not quantify possible systematic offsets between the optically thick jet base and the stellar center of mass; this assumption is load-bearing for the interpretation of tangential motion and concordance with large-scale flows.

    Authors: We acknowledge that the interpretation assumes the geodetic VLBI core position traces the stellar center of mass. The 28-year time series and 1-norm/bootstrap procedure already suppress the influence of transient jet components. Published multi-frequency VLBI studies of M87 indicate core shifts at 8 GHz are ≲ 0.1 mas and stable over decades, well below the measured proper-motion signal. We will add a concise paragraph in the discussion citing these constraints and noting the residual systematic as a caveat, but we cannot derive a new quantitative bound from the existing data alone. revision: partial

Circularity Check

0 steps flagged

No circularity: direct observational measurement converted via standard formulas and adopted distance

full rationale

The paper reports a direct astrometric measurement of the radio core proper motion from 28 years of VLBI data using 1-norm optimization and bootstrapping. The tangential velocity is computed from this proper motion and an externally adopted distance of 16.1 Mpc via the standard conversion v_t = 4.74 × μ(mas yr⁻¹) × d(kpc). The peculiar velocity vector is formed by combining the transverse component with the radial peculiar velocity (observed radial velocity minus H₀d). These steps rely on external reference frames (ICRF, CMB) and standard astronomical formulas without any self-referential definitions, fitted inputs renamed as predictions, or results that reduce to the inputs by construction. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the AGN core traces the galaxy's center-of-mass motion and on an externally adopted distance; no new free parameters are fitted beyond the astrometric solution itself.

free parameters (1)
  • distance to M87
    Adopted value of 16.1 Mpc used to convert angular proper motion into linear velocity; uncertainty not propagated in the reported peculiar velocity.
axioms (2)
  • domain assumption The position of the radio core represents the bulk motion of the galaxy
    Standard assumption in AGN astrometry but not independently verified in the abstract.
  • standard math The ICRF and CMB define the inertial and rest frames respectively
    Standard reference frames used for position angle and peculiar velocity subtraction.

pith-pipeline@v0.9.0 · 5584 in / 1376 out tokens · 47123 ms · 2026-05-12T01:01:01.178722+00:00 · methodology

discussion (0)

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Works this paper leans on

31 extracted references · 31 canonical work pages · 1 internal anchor

  1. [1]

    J., Perlman, E

    Batcheldor, D., Robinson, A., Axon, D. J., Perlman, E. S., & Merritt, D. 2010, ApJL, 717, L6, doi: 10.1088/2041-8205/717/1/L6 B¨ ohringer, H., Briel, U. G., Schwarz, R. A., et al. 1994, Nature, 368, 828, doi: 10.1038/368828a0

    work page doi:10.1088/2041-8205/717/1/l6 2010

  2. [2]

    2011, MNRAS, 411, 955, doi: 10.1111/j.1365-2966.2010.17731.x

    Cappellari, M., Emsellem, E., Krajnovi´ c, D., et al. 2011, MNRAS, 413, 813, doi: 10.1111/j.1365-2966.2010.18174.x

    work page doi:10.1111/j.1365-2966.2010.18174.x 2011

  3. [3]

    V., Secrest, N

    Cigan, P., Makarov, V. V., Secrest, N. J., et al. 2024, ApJS, 274, 28, doi: 10.3847/1538-4365/ad6772 de Grijs, R., & Bono, G. 2020, ApJS, 246, 3, doi: 10.3847/1538-4365/ab5711 de Vaucouleurs, G., de Vaucouleurs, A., & Corwin, J. R. 1976, Second reference catalogue of bright galaxies, 1976, 0 Space Velocity of Messier 8711 Event Horizon Telescope Collabora...

    work page doi:10.3847/1538-4365/ad6772 2024

  4. [4]

    2024, A&A, 681, A79, doi: 10.1051/0004-6361/202347932

    Alberdi, A., et al. 2024, A&A, 681, A79, doi: 10.1051/0004-6361/202347932

    work page doi:10.1051/0004-6361/202347932 2024

  5. [5]

    T., Bouman, K

    Feng, B. T., Bouman, K. L., & Freeman, W. T. 2024, ApJ, 975, 201, doi: 10.3847/1538-4357/ad737f Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272 Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021a, A&A, 649, A1, doi: 10.1051/0004-6361/202039657 Gaia Collaboration, Klioner, S. A....

    work page doi:10.3847/1538-4357/ad737f 2024

  6. [6]

    Gordon, D., de Witt, A., & Jacobs, C. S. 2023, AJ, 165, 49, doi: 10.3847/1538-3881/aca65b GRAVITY Collaboration, Abuter, R., Amorim, A., et al. 2019, A&A, 625, L10, doi: 10.1051/0004-6361/201935656

    work page doi:10.3847/1538-3881/aca65b 2023

  7. [7]

    2008, ApJ, 678, 780, doi: 10.1086/586877

    Gualandris, A., & Merritt, D. 2008, ApJ, 678, 780, doi: 10.1086/586877

    work page doi:10.1086/586877 2008

  8. [8]

    V., & Gottl¨ ober, S

    Klypin, A., Hoffman, Y., Kravtsov, A. V., & Gottl¨ ober, S. 2003, ApJ, 596, 19, doi: 10.1086/377574

    work page doi:10.1086/377574 2003

  9. [9]

    M., & Makarov, V

    Kopeikin, S. M., & Makarov, V. V. 2006, AJ, 131, 1471, doi: 10.1086/500170

    work page doi:10.1086/500170 2006

  10. [10]

    2003, A&A, 404, 743, doi: 10.1051/0004-6361:20030560

    Kovalevsky, J. 2003, A&A, 404, 743, doi: 10.1051/0004-6361:20030560

    work page doi:10.1051/0004-6361:20030560 2003

  11. [11]

    X., Webster, A

    Lahav, O., Santiago, B. X., Webster, A. M., et al. 1998, arXiv e-prints, astro, doi: 10.48550/arXiv.astro-ph/9809343 L´ opez-Navas, E., & Prieto, M. A. 2018, MNRAS, 480, 4099, doi: 10.1093/mnras/sty2148

    work page internal anchor Pith review doi:10.48550/arxiv.astro-ph/9809343 1998

  12. [12]

    V., Cigan, P., Gordon, D., et al

    Makarov, V. V., Cigan, P., Gordon, D., et al. 2024a, ApJL, 977, L14, doi: 10.3847/2041-8213/ad94f1

    work page doi:10.3847/2041-8213/ad94f1 2041

  13. [13]

    2024b, PASP, 136, 054503, doi: 10.1088/1538-3873/ad4b9f

    Gordon, D. 2024b, PASP, 136, 054503, doi: 10.1088/1538-3873/ad4b9f

    work page doi:10.1088/1538-3873/ad4b9f

  14. [14]

    W., & Venn, K

    McConnachie, A. W., & Venn, K. A. 2020, Research Notes of the American Astronomical Society, 4, 229, doi: 10.3847/2515-5172/abd18b

    work page doi:10.3847/2515-5172/abd18b 2020

  15. [15]

    P., Cˆ ot´ e, P., et al

    Mei, S., Blakeslee, J. P., Cˆ ot´ e, P., et al. 2007, ApJ, 655, 144, doi: 10.1086/509598 Mo´ or, A., Frey, S., Lambert, S. B., Titov, O. A., & Bakos, J. 2011, AJ, 141, 178, doi: 10.1088/0004-6256/141/6/178

    work page doi:10.1086/509598 2007

  16. [16]

    2013, in IAU Symposium, Vol

    Mould, J. 2013, in IAU Symposium, Vol. 289, Advancing the Physics of Cosmic Distances, ed. R. de Grijs, 262–268, doi: 10.1017/S1743921312021527

    work page doi:10.1017/s1743921312021527 2013

  17. [17]

    2020, A&A, 634, A38, doi: 10.1051/0004-6361/201936586

    Nalewajko, K., Sikora, M., & R´ o˙ za´ nska, A. 2020, A&A, 634, A38, doi: 10.1051/0004-6361/201936586

    work page doi:10.1051/0004-6361/201936586 2020

  18. [18]

    W., Jord´ an, A., Blakeslee, J

    Peng, E. W., Jord´ an, A., Blakeslee, J. P., et al. 2009, ApJ, 703, 42, doi: 10.1088/0004-637X/703/1/42

    work page doi:10.1088/0004-637x/703/1/42 2009

  19. [19]

    J., Welch, D

    Pierce, M. J., Welch, D. L., McClure, R. D., et al. 1994, Nature, 371, 385, doi: 10.1038/371385a0 Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910

    work page doi:10.1038/371385a0 1994

  20. [20]

    2007, arXiv e-prints, arXiv:0710.1338, doi: 10.48550/arXiv.0710.1338

    Pretorius, F. 2007, arXiv e-prints, arXiv:0710.1338, doi: 10.48550/arXiv.0710.1338

    work page doi:10.48550/arxiv.0710.1338 2007

  21. [21]

    2009, Phys

    Quercellini, C., Quartin, M., & Amendola, L. 2009, Phys. Rev. Lett., 102, 151302, doi: 10.1103/PhysRevLett.102.151302

    work page doi:10.1103/physrevlett.102.151302 2009

  22. [22]

    B., Ibata, R., Reyl´ e, C., et al

    Salomon, J. B., Ibata, R., Reyl´ e, C., et al. 2021, MNRAS, 507, 2592, doi: 10.1093/mnras/stab2253 Sch¨ onrich, R., Binney, J., & Dehnen, W. 2010, MNRAS, 403, 1829, doi: 10.1111/j.1365-2966.2010.16253.x

    work page doi:10.1093/mnras/stab2253 2021

  23. [23]

    J., Tully, R

    Shaya, E. J., Tully, R. B., Hoffman, Y., & Pomar` ede, D. 2017, ApJ, 850, 207, doi: 10.3847/1538-4357/aa9525

    work page doi:10.3847/1538-4357/aa9525 2017

  24. [24]

    A., Galazutdinova, O

    Tikhonov, N. A., Galazutdinova, O. A., & Karataeva, G. M. 2019, Astrophysical Bulletin, 74, 257, doi: 10.1134/S1990341319030027

    work page doi:10.1134/s1990341319030027 2019

  25. [25]

    2013a, VizieR Online Data Catalog: Fitted proper motions for the DR solution (Titov+, 2013),, VizieR On-line Data Catalog: J/A+A/559/A95

    Titov, O., & Lambert, S. 2013a, VizieR Online Data Catalog: Fitted proper motions for the DR solution (Titov+, 2013),, VizieR On-line Data Catalog: J/A+A/559/A95. Originally published in: 2013A&A...559A..95T doi: 10.26093/cds/vizier.35590095

    work page doi:10.26093/cds/vizier.35590095 2013

  26. [26]

    2013b, A&A, 559, A95, doi: 10.1051/0004-6361/201321806

    Titov, O., & Lambert, S. 2013b, A&A, 559, A95, doi: 10.1051/0004-6361/201321806

    work page doi:10.1051/0004-6361/201321806

  27. [27]

    B., & Gontier, A

    Titov, O., Lambert, S. B., & Gontier, A. M. 2011, VizieR Online Data Catalog: Proper motions of 555 quasars from VLBI (Titov+, 2011),, VizieR On-line Data Catalog: J/A+A/529/A91. Originally published in: 2011A&A...529A..91T doi: 10.26093/cds/vizier.35290091

    work page doi:10.26093/cds/vizier.35290091 2011

  28. [28]

    E., & Darling, J

    Truebenbach, A. E., & Darling, J. 2017, ApJS, 233, 3, doi: 10.3847/1538-4365/aa9026

    work page doi:10.3847/1538-4365/aa9026 2017

  29. [29]

    , keywords =

    Tully, R. B., Courtois, H. M., & Sorce, J. G. 2016, AJ, 152, 50, doi: 10.3847/0004-6256/152/2/50

    work page doi:10.3847/0004-6256/152/2/50 2016

  30. [30]

    B., & Shaya, E

    Tully, R. B., & Shaya, E. J. 1984, ApJ, 281, 31, doi: 10.1086/162073

    work page doi:10.1086/162073 1984

  31. [31]

    , archivePrefix = "arXiv", eprint =

    Junor, W. 2018, ApJ, 855, 128, doi: 10.3847/1538-4357/aaafcc

    work page doi:10.3847/1538-4357/aaafcc 2018